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Triangles, Tropes, and Τὰ Τοιαʋ̃τα: a Platonic Trope Theory

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Triangles, Tropes, and Τὰ Τοιαʋ̃τα: a Platonic Trope Theory CHRISTOPHER BUCKELS | 9 Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory Christopher Buckels University of California [email protected] ABSTRACT A standard interpretation of Plato’s metaphys- ics holds that sensible particulars are images of Forms. Such particulars are fairly indepen- dent, like Aristotelian substances. I argue that this is incorrect: Platonic particulars are not Form images but aggregates of Form images, which are property-instances (tropes). Timaeus 49e-50a focuses on “this-suches” (toiauta) and even goes so far as to claim that they compose other things. I argue that Form images are this- suches, which are tropes. I also examine the geometrical account, showing that the geomet- rical constituents of the elements are also Form images. Thus everything in the sensible world is composed of tropes. Keywords : Particulars; Tropes; Plato; Timaeus; Substance; Metaphysics; Greek Philosophy https://doi.org/10.14195/2183-4105_18_1 10 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory 1. INTRODUCTION will explain and defend the second syllogism (which may be understood as laying out a con­ In the Timaeus, Plato offers an account sequence of the first syllogism), and the fourth of the world whereby macroscopic physical part will consider objections. As will become objects are composed of microscopic three­ clear in the paper, I take Timaeus’ metaphysics ­dimensional objects, which are, in turn, of particulars to be a version of a trope theory, composed of two­‑dimensional objects. Most, and so I take τὰ τοιαῦτα to be tropes, but I will if not all, properties of macroscopic objects are defend this claim in the fourth part; I will also explained by properties of microscopic objects, consider the traditional account of particulars which are in turn explained by the configu­ in the Timaeus whereby Form images are bod­ ration of two­‑dimensional objects. We seem ies (i.e., physical objects) rather than tropes. to have a completely reductionist, naturalist Let me begin by giving an initial character­ account of the world; why, then, is it accompa­ ization of a Platonic trope theory. Tropes are nied by supernatural entities such as Platonic often used to avoid commitment to universals; Forms? While I will explain why Forms are the universal or Form Whiteness, for example, crucial for the account of particulars in the could be the set of all whiteness tropes. Most Timaeus, I will be focusing not on Forms, but trope theories, therefore, are nominalist theo­ on sensible particulars, the three­‑dimensional ries. Timaeus is not, of course, a trope nomi­ objects we bump into on a day­‑to­‑day basis, nalist; his tropes coexist with transcendent as well as their constituents. I will argue that universals, Forms.1 In his terms, a trope is a Plato does not take these particulars as basic “this­‑such” (τὸ τοιοῦτον) or Form image — constituents of the physical world, but that the a trope­‑theoretic interpretation of Timaeus’ ultimate constituents of Timaeus’ sensible par­ ontology is thus not anachronistic, since he ticulars are what metaphysicians call tropes, himself introduces tropes, as I will show, albeit or property­‑instances; Timaeus calls them τὰ under the name of “this­‑suches” (τὰ τοιαῦτα).2 τοιαῦτα, “this­‑suches.” My argument follows: When one feels hot, one does not feel heat in general but a particular heat, this ­heat: a heat 1. Each thing that comes to be is τὸ trope. Thus the heat in a given fire is not a τοιοῦτον (this ­such). repeatable entity or “immanent universal,” 2. All and only things that come to be but a particular entity, distinct from each are images of Forms. other instance of heat. This is what I mean by 3. Therefore, τὰ τοιαῦτα (this­‑suches) are a trope: a particular, non­‑repeatable instance images of Forms. of a property. 4. Triangles are τὰ τοιαῦτα or are con­ While trope theorists generally take tropes structed from τὰ τοιαῦτα. to be fundamental entities out of which uni­ 5. All bodies are constructed from tri­ versals may be constructed, Timaeus’ tropes angles. are dependent upon transcendent universals, 6. Therefore, all bodies are constructed as “Form image” implies. So a heat trope is an from τὰ τοιαῦτα (images of Forms). image of Heat, and there can be many distinct images of the same Form of Heat, each image The second part of the paper will explain coming to be and then perishing as something and defend the first syllogism, the third part becomes and then ceases to be hot. I take Forms CHRISTOPHER BUCKELS | 11 to be immutable, non­‑spatiotemporal entities The context is a puzzle about the elements, that are universals insofar as they explain com­ which seem to be too unstable to admit of be­ monality in resembling things. Heat explains ing called any one thing, since they could, at the commonality in two hot things precisely any moment, change into different elements. by having an image of itself — numerically Should we say, when pointing at a bonfire, for distinct but qualitatively identical — in each example, ‘fire is this sort of thing’ rather than hot thing; i.e., two hot things resemble each ‘fire is this thing’, or should we say ‘this sort of other because each contains a heat trope. thing is fire’ instead of ‘this thing is fire’? A trope­‑bundle theorist would say that However one wishes to settle this dispute, sensible particulars are wholly constituted we can focus on “this­‑such” and identify two by tropes. Fire is a bundle of heat, color, etc. main interpretations of τὸ τοιοῦτον in the pas­ While I do not here defend a Platonic trope­ sage. The first, dubbed the ‘traditional transla­ bundle theory, my arguments naturally lead tion’ by its adherents, claims that τὰ τοιαῦτα to such an interpretation. My trope­‑theoretic are “temporary characteristics” rather than interpretation of the Timaeus differs from tra­ “self­‑subsistent” things (Zeyl 2000 lviii, n. 18). ditional interpretations in that it takes tropes The second, which Zeyl calls the ‘alternative rather than sensible particulars as images of translation,’ takes τὰ τοιαῦτα to be “distinct Forms. Instead of holding that sensible par­ and self­‑identical characteristics” or “recurrent, ticulars have their properties by participat­ stable, and determinate characters” (following ing in Forms, a trope­‑theoretic interpretation Cherniss 1954). I propose, for now, to follow a holds that sensible particulars have properties middle ground, calling them “characteristics;” by having tropes as constituents. Thus Forms we will leave aside whether they are “tempo­ and their images — in contemporary terms, rary” or “recurrent, stable, and determinate.” transcendent universals and tropes — play We are left with quite a bit of agreement. On the central role in Plato’s explanation of the the one hand, these characteristics are tempo­ sensible world, rather than sensible particulars rary in at least one sense: they may be at a cer­ playing the starring role. tain place for only a short time, and that place may be occupied by a different characteristic at any time. Thus the fiery characteristic may 2. τὰ τοιαʋ ̃τα be replaced by a watery characteristic at any moment. On the other hand, these character­ 2.1. EACH THING THAT COMES TO BE IS istics are stable and determinate in at least one τὰ τοιαʋ ̃τα sense: for as long as each exists—which may be only an instant—it is that characteristic and not Timaeus introduces τὰ τοιαῦτα at 49d5, some other. It may be identified as belonging in the midst of a very controversial passage.3 to a certain kind. So the fiery characteristic is At the heart of the controversy is whether we fiery for as long as it exists, even if is replaced should take Timaeus to say, “fire is τὸ τοιοῦτον by a watery characteristic in but a moment. (“this such” or “this sort of thing”), rather than On either translation, Timaeus generalizes τοῦτο (“this” or “that”)”, or, “τὸ τοιοῦτον, not his conclusions to “everything that comes to τοῦτο, is fire.” The debate is thus over which be” (49e7). Thus every generated entity is a terms are subjects and which are predicates. characteristic, not a ‘thing;’ the characteristic 12 | Triangles, Tropes, and τὰ τοιαʋ ̃τα: A Platonic Trope Theory may be replaced at any time by another char­ that it is an image (τόνδε τὸν κόσμον εἰκόνα acteristic, but it remains what it is as long as τινὸς εἶναι, 29b1­‑2), viz., an image of an eter­ it is. If we generalize this claim, it applies to nal, changeless model (παράδειγμα, 29a2­‑b2). any characteristic, e.g., that of being a garbage So the demiurge, a divine craftsman, looks to truck, not just to elements. And there is no rea­ Being in order to make the universe, which is son to think it does not apply completely gen­ an image of the Living Being that contains all erally, since Timaeus gives “hot” and “white” the intelligible living beings as parts just as as further examples. Even if we think that the the universe contains us and all the other vis­ properties of being hot and being white are ible creatures (30c2­‑d1). I take the “intelligible suggested from our discussion of fire, they are living beings” to be Forms of animal species, widely applicable to macroscopic objects, and e.g., the Form of Human Being, the Form of we are given no reason to restrict their use to Goat, etc. The Living Being that contains all describing elements. In fact, Timaeus cannot be the others would be, then, the Form of Living restricting his argument to elements, since he Being, i.e., the transcendent universal that ex­ extends it to “anything you can point to,” and plains what all living beings have in common.6 it is not, strictly speaking, possible to point to Thus we have reason to identify Being with an element, since they are microscopic particles Forms, an identification that is confirmed, (we can point to some fire or water, but these e.g., at 51d3­‑52a4.
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